My math teacher taught me not only calculus, but also when and who got up to what. It doesn't have to take a long time, but a bit of context helps a lot. Euler went to Russia and yada yada bridges graphs etc.
Same goes for all science disciplines. You need to have a rough idea that Darwin worked in the 19th century, that much of thermo came about in the late 19th century, that quantum is a 20th century thing. You need to know what people were wondering about, and what experiments they came up with.
I've been listening to a lot of audio courses lately, and those little nuggets really help to understand things.
The point of the little stories such as how Watson and Crick came up with the double helix is to help recall. It's hard to remember dry facts, much easier to remember stories. People are kinda built that way.
Yes Yes Yes! One of the best math books I ever read, "Math for the Millions" by Lancelot Hogben taught each math topic as something that was discovered as civilization grew to have more complex problems.
I strongly believe math should be taught with the science that motivated its development- calculus should be taught with classical mechanics. But I'm less sure the history of science is worthwhile.
The problem is opportunity cost. Schools (highschool, college intro physics) spend a great deal of time discussing previous models of the atom. What's the value of teaching Thomson's plum pudding model of the atom, really? They could start with the current model and list all of the observations/experiments that have shown the model to be useful. Previous models could be relegated to an appendix, or a history class.
This would free up time to more comprehensively discuss 20th and 21st century physics, which are sorely neglected at this level.
The value of teaching Thomson's plum pudding model of the atom is to understand the evolution of ideas. It also helps the young minds understand that solving problems is often messy and we have to revisit our understanding of scientific models as new facts emerge. It might be obvious to you but the young students would feel that solutions would come in a single shot.
Ideally if the students have strong basics 20th and 21st century physics should be tried by the students themselves.
I think there is value in teaching that there have been prior models (but more energy should be spent on the current thinking) because it shows that good scientists are constantly researching and revising their ideas as they get more information. Science is never done.
To be clear I agree there's value, I just don't think the value is as high as the other things that could be taught in that time.
I think appendices are really a good solution here. Those who are curious can read them- I know I would have. Those who aren't, can stick to focusing on the current model.
I'm not sure I agree. I think that understanding that knowledge is never done, and that science is about exploring new ideas and questioning our current understanding is much more important to the layperson than knowing how atoms are structured.
I also think that couching science as a journey--a mystery to be solved, with clues and red herrings along the way--will help to get students interested in learning the details. (This is all just my gut instinct; I have no experience in science education, so I might not know what I'm talking about).
Yeah, calculus seems really abstract and pointless until you realise that it's 90% of physics. At school they shy away from calculus so much that you just do a version of physics where they've simplified away the calculus, which is extremely confusing.
Hearing their stories communicates to you the existence of the millenia-wide fellowship of truthseekers, and that what you are receiving is not just fodder for tests---it is your inheritance.
> how Watson and Crick came up with the double helix
s/came up with/stole the idea from looking at Rosalind Franklin's X-ray data/
To be fair, both Watson and Crick strongly insisted she also get the Nobel, but she'd tragically passed a way shortly before the award was announced, and the rules are very clear about no posthumous awards. Still, it's sad that we don't teach Franklin's role.
I have never, not once, come across a discussion of Watson and Crick that did not also talk about Franklin's role.
Even when I was in high school back in the 80's, her contribution was front and center, along with the other two. Can we please let the myth that somehow her contribution is forgotten and not taught to die?
Always the headline is Watson and Crick. Not Franklin with some minor assistance from ...
Franklin is being brought into the "Watson and Crick" discussion. Rather than it being Franklin first, foremost and clearly most important. Let's not airbrush that her research was provided to Watson and Crick who claimed the glory without her consent.
No one forgets that her data was taken/stolen. The fact of the matter is that she didn't come up with the final structure given her brilliant experimental work and results. The history of science is littered with forgotten people who were scooped of the glory just short of the line. Franklin is very well recognised given that she didn't discover the structure of DNA.
I agree that historical context should be taught in classes. I wrote a Master's adding plenty of historical notes about "why" this and that approximation was thought of, and proposed. Sometimes it doesn't take much - just reading the early Schrödinger papers can give you an idea of his train of thought. It really helps make sense out of theory, for me.
"Euler went to Russia and yada yada bridges graphs"
I know little of this history, but is there any link between him going to Russia and him solving the seven bridges of Königsberg problem?
I'm asking because I don't know whether Euler ever visited Königsberg and because Königsberg is in Russia now (renamed to Kaliningrad after WWII), but was in Prussia at the time.
He went to work in St Petersberg, which is just up the coast. No idea if he sailed or drove, but it seems quite likely to have been on his way regardless of where in Europe he was before (Switzerland?).
"Euler left Basel on 5 April 1727. He travelled down the Rhine by boat, crossed the German states by post wagon, then by boat from Lübeck arriving in St Petersburg on 17 May 1727."
Still inconclusive, but given that we know this, I would say chances are non-zero that the sources this was derived from spell out where that ship made stops.
One could also look at his journeys from Leningrad to Berlin and, years later, back, but both were after his publication on the 7 bridges problem.
Someone probably drove the vehicle in question for Euler but:
b.2.b One who drives a vehicle or the animal that draws it; a charioteer, coachman, cabman, etc.; also, one who drives a locomotive engine. (Often with defining word prefixed, as cab-driver, engine-driver, etc., for which see the first element.) [...]
c 1450 St. Cuthbert (Surtees) 6016 All þe dryuers ware agaste þat þe sledd suld ga our faste. 1581 Savile Tacitus 93 (R.) Buffons, stage-players, and charet drivers. 1725 Pope Odyss. xiii. 99 Fiery coursers in the rapid race Urg'd by fierce drivers thro' the dusty space. [...]
I'll be the devils advocate. Why? I can understand calculus perfectly fine without understanding how people got there. In fact, I'd argue much of what you learn before call--in the order of discovery--actively hinders understanding.
Because advancing science and mathematics is not a straight line but full frustrations inside a cloud of uncertainty and anxiety. It is important to appreciate what the world looked like before the discovery and how someone tackled a problem to change this view of the world because when you yourself make discoveries you will be in the exact same situation.
However if all you care is to use what has been discovered, which is becoming less and less valuable, then you don't need to learn history of mathematics and science.
Although this is not good evidence but rather an anecdote, I cannot remember any significant person who has made fundamental contributions to mathematics or science that was completely ignorant of the history of the field.
Let me give an example from calculus - a continuous function. How do you define the concept? The definiton of the concept changed quite a lot in the past 250 years or so. (Please take the following explanation with a grain of salt, I am not writing a thesis on the topic, just pointing out stuff.)
For Euler, continuous function was pretty much intuitive notion. He only composed functions with only occasional point discontinuities, so it wasn't a big deal for him to even not have a proper definition.
Then people like Bolzano and Dirichlet came along and realized they need a better definition, because there can be some really weird cases. So they formalized the continuity with limits (which is typical way how to define it in basic calculus).
Later yet, people understood better what it means to be a real number by looking at notions such as countability and measurability. While this doesn't affect continuity itself, it does affect understanding of what is a real fuction.
Then came more abstraction, to metric spaces and eventually topological spaces, which redefined "continuous function" yet again as a morphism between topological spaces.
Another shift in thinking about continuity happened when theory of distributions was invented. This actually completely reverses the intuition - instead of properly definining reals and then on top of real function define what it means to be continuous, you define the "function" itself in an entirely different way, in which the continuity becomes somewhat irrelevant.
Finally, modern mathematics is quite obsessed with category theory and various ways to make everything into some algebra. In a way, we care less what reals really are, only what we can do with them (or their sets).
So I think to understand the intuitive relation of all these different definitions, you need to understand a little bit of history.
Many people will find it easier to follow maths lessons if there are a few bits of history sprinkled in here and there. It adds a human element and honoring the great ones hundreds of years (or even millennia) after they are dead serves as an implicit demonstration of how important their discoveries are to us. Not a terribly powerful demonstration, but less futile than repeatedly yelling "hey, this is important!"
Also, mathematical concepts don't come with natural names attached. But we need consistent labels for successful communication. It's much easier to not confuse those labels if you know a bit about the history that led to the naming.
My math teacher taught me not only calculus, but also when and who got up to what. It doesn't have to take a long time, but a bit of context helps a lot. Euler went to Russia and yada yada bridges graphs etc.
Same goes for all science disciplines. You need to have a rough idea that Darwin worked in the 19th century, that much of thermo came about in the late 19th century, that quantum is a 20th century thing. You need to know what people were wondering about, and what experiments they came up with.
I've been listening to a lot of audio courses lately, and those little nuggets really help to understand things.
The point of the little stories such as how Watson and Crick came up with the double helix is to help recall. It's hard to remember dry facts, much easier to remember stories. People are kinda built that way.